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<div class="header">
  <div class="summary">
<a href="classEigen_1_1LLT-members.html">List of all members</a> &#124;
<a href="#pub-methods">Public Member Functions</a>  </div>
  <div class="headertitle">
<div class="title">Eigen::LLT&lt; MatrixType_, UpLo_ &gt; Class Template Reference<div class="ingroups"><a class="el" href="group__DenseLinearSolvers__chapter.html">Dense linear problems and decompositions</a> &raquo; <a class="el" href="group__DenseLinearSolvers__Reference.html">Reference</a> &raquo; <a class="el" href="group__Cholesky__Module.html">Cholesky module</a></div></div>  </div>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><h3>template&lt;typename MatrixType_, int UpLo_&gt;<br />
class Eigen::LLT&lt; MatrixType_, UpLo_ &gt;</h3>

<p>Standard Cholesky decomposition (LL^T) of a matrix and associated features. </p>
<dl class="tparams"><dt>Template Parameters</dt><dd>
  <table class="tparams">
    <tr><td class="paramname">MatrixType_</td><td>the type of the matrix of which we are computing the LL^T Cholesky decomposition </td></tr>
    <tr><td class="paramname">UpLo_</td><td>the triangular part that will be used for the decomposition: Lower (default) or Upper. The other triangular part won't be read.</td></tr>
  </table>
  </dd>
</dl>
<p>This class performs a LL^T Cholesky decomposition of a symmetric, positive definite matrix A such that A = LL^* = U^*U, where L is lower triangular.</p>
<p>While the Cholesky decomposition is particularly useful to solve selfadjoint problems like D^*D x = b, for that purpose, we recommend the Cholesky decomposition without square root which is more stable and even faster. Nevertheless, this standard Cholesky decomposition remains useful in many other situations like generalised eigen problems with hermitian matrices.</p>
<p>Remember that Cholesky decompositions are not rank-revealing. This <a class="el" href="classEigen_1_1LLT.html" title="Standard Cholesky decomposition (LL^T) of a matrix and associated features.">LLT</a> decomposition is only stable on positive definite matrices, use <a class="el" href="classEigen_1_1LDLT.html" title="Robust Cholesky decomposition of a matrix with pivoting.">LDLT</a> instead for the semidefinite case. Also, do not use a Cholesky decomposition to determine whether a system of equations has a solution.</p>
<p>Example: </p><div class="fragment"><div class="line"><a class="code" href="group__matrixtypedefs.html#ga99b41a69f0bf64eadb63a97f357ab412">MatrixXd</a> A(3,3);</div>
<div class="line">A &lt;&lt; 4,-1,2, -1,6,0, 2,0,5;</div>
<div class="line">cout &lt;&lt; <span class="stringliteral">&quot;The matrix A is&quot;</span> &lt;&lt; endl &lt;&lt; A &lt;&lt; endl;</div>
<div class="line"> </div>
<div class="line">LLT&lt;MatrixXd&gt; lltOfA(A); <span class="comment">// compute the Cholesky decomposition of A</span></div>
<div class="line"><a class="code" href="group__matrixtypedefs.html#ga99b41a69f0bf64eadb63a97f357ab412">MatrixXd</a> L = lltOfA.matrixL(); <span class="comment">// retrieve factor L  in the decomposition</span></div>
<div class="line"><span class="comment">// The previous two lines can also be written as &quot;L = A.llt().matrixL()&quot;</span></div>
<div class="line"> </div>
<div class="line">cout &lt;&lt; <span class="stringliteral">&quot;The Cholesky factor L is&quot;</span> &lt;&lt; endl &lt;&lt; L &lt;&lt; endl;</div>
<div class="line">cout &lt;&lt; <span class="stringliteral">&quot;To check this, let us compute L * L.transpose()&quot;</span> &lt;&lt; endl;</div>
<div class="line">cout &lt;&lt; L * L.transpose() &lt;&lt; endl;</div>
<div class="line">cout &lt;&lt; <span class="stringliteral">&quot;This should equal the matrix A&quot;</span> &lt;&lt; endl;</div>
<div class="ttc" id="agroup__matrixtypedefs_html_ga99b41a69f0bf64eadb63a97f357ab412"><div class="ttname"><a href="group__matrixtypedefs.html#ga99b41a69f0bf64eadb63a97f357ab412">Eigen::MatrixXd</a></div><div class="ttdeci">Matrix&lt; double, Dynamic, Dynamic &gt; MatrixXd</div><div class="ttdoc">Dynamic×Dynamic matrix of type double.</div><div class="ttdef"><b>Definition:</b> Matrix.h:501</div></div>
</div><!-- fragment --><p> Output: </p><pre class="fragment">The matrix A is
 4 -1  2
-1  6  0
 2  0  5
The Cholesky factor L is
    2     0     0
 -0.5   2.4     0
    1 0.209  1.99
To check this, let us compute L * L.transpose()
 4 -1  2
-1  6  0
 2  0  5
This should equal the matrix A
</pre><p><b>Performance:</b> for best performance, it is recommended to use a column-major storage format with the Lower triangular part (the default), or, equivalently, a row-major storage format with the Upper triangular part. Otherwise, you might get a 20% slowdown for the full factorization step, and rank-updates can be up to 3 times slower.</p>
<p>This class supports the <a class="el" href="group__InplaceDecomposition.html">inplace decomposition </a> mechanism.</p>
<p>Note that during the decomposition, only the lower (or upper, as defined by UpLo_) triangular part of A is considered. Therefore, the strict lower part does not have to store correct values.</p>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="classEigen_1_1MatrixBase.html#a90c45f7a30265df792d5aeaddead2635">MatrixBase::llt()</a>, <a class="el" href="classEigen_1_1SelfAdjointView.html#a405e810491642a7f7b785f2ad6f93619">SelfAdjointView::llt()</a>, class <a class="el" href="classEigen_1_1LDLT.html" title="Robust Cholesky decomposition of a matrix with pivoting.">LDLT</a> </dd></dl>
</div><div id="dynsection-0" onclick="return toggleVisibility(this)" class="dynheader closed" style="cursor:pointer;">
  <img id="dynsection-0-trigger" src="closed.png" alt="+"/> Inheritance diagram for Eigen::LLT&lt; MatrixType_, UpLo_ &gt;:</div>
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<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-methods"></a>
Public Member Functions</h2></td></tr>
<tr class="memitem:aa6ba8440554d9837b2bdb44b4c80c378"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="classEigen_1_1LLT.html">LLT</a> &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1LLT.html#aa6ba8440554d9837b2bdb44b4c80c378">adjoint</a> () const EIGEN_NOEXCEPT</td></tr>
<tr class="separator:aa6ba8440554d9837b2bdb44b4c80c378"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a9dde013e51ed2b5cf2134daa3887d1e3"><td class="memTemplParams" colspan="2">template&lt;typename InputType &gt; </td></tr>
<tr class="memitem:a9dde013e51ed2b5cf2134daa3887d1e3"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1LLT.html">LLT</a>&lt; MatrixType, UpLo_ &gt; &amp;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1LLT.html#a9dde013e51ed2b5cf2134daa3887d1e3">compute</a> (const <a class="el" href="structEigen_1_1EigenBase.html">EigenBase</a>&lt; InputType &gt; &amp;a)</td></tr>
<tr class="separator:a9dde013e51ed2b5cf2134daa3887d1e3"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a1d05e5f1a15692959eb9e09d8959a5d5"><td class="memItemLeft" align="right" valign="top"><a class="el" href="group__enums.html#ga85fad7b87587764e5cf6b513a9e0ee5e">ComputationInfo</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1LLT.html#a1d05e5f1a15692959eb9e09d8959a5d5">info</a> () const</td></tr>
<tr class="memdesc:a1d05e5f1a15692959eb9e09d8959a5d5"><td class="mdescLeft">&#160;</td><td class="mdescRight">Reports whether previous computation was successful.  <a href="classEigen_1_1LLT.html#a1d05e5f1a15692959eb9e09d8959a5d5">More...</a><br /></td></tr>
<tr class="separator:a1d05e5f1a15692959eb9e09d8959a5d5"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ae013aeead8f1f48c536ec0c3f1342bbd"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1LLT.html#ae013aeead8f1f48c536ec0c3f1342bbd">LLT</a> ()</td></tr>
<tr class="memdesc:ae013aeead8f1f48c536ec0c3f1342bbd"><td class="mdescLeft">&#160;</td><td class="mdescRight">Default Constructor.  <a href="classEigen_1_1LLT.html#ae013aeead8f1f48c536ec0c3f1342bbd">More...</a><br /></td></tr>
<tr class="separator:ae013aeead8f1f48c536ec0c3f1342bbd"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a9634e284ac5646451dce3d97b39a19da"><td class="memTemplParams" colspan="2">template&lt;typename InputType &gt; </td></tr>
<tr class="memitem:a9634e284ac5646451dce3d97b39a19da"><td class="memTemplItemLeft" align="right" valign="top">&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1LLT.html#a9634e284ac5646451dce3d97b39a19da">LLT</a> (<a class="el" href="structEigen_1_1EigenBase.html">EigenBase</a>&lt; InputType &gt; &amp;matrix)</td></tr>
<tr class="memdesc:a9634e284ac5646451dce3d97b39a19da"><td class="mdescLeft">&#160;</td><td class="mdescRight">Constructs a <a class="el" href="classEigen_1_1LLT.html" title="Standard Cholesky decomposition (LL^T) of a matrix and associated features.">LLT</a> factorization from a given matrix.  <a href="classEigen_1_1LLT.html#a9634e284ac5646451dce3d97b39a19da">More...</a><br /></td></tr>
<tr class="separator:a9634e284ac5646451dce3d97b39a19da"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a3ee367058bfa84f9b095bfc6015df08e"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1LLT.html#a3ee367058bfa84f9b095bfc6015df08e">LLT</a> (<a class="el" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> <a class="el" href="structEigen_1_1EigenBase.html#ae106171b6fefd3f7af108a8283de36c9">size</a>)</td></tr>
<tr class="memdesc:a3ee367058bfa84f9b095bfc6015df08e"><td class="mdescLeft">&#160;</td><td class="mdescRight">Default Constructor with memory preallocation.  <a href="classEigen_1_1LLT.html#a3ee367058bfa84f9b095bfc6015df08e">More...</a><br /></td></tr>
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<tr class="memitem:afb5490bbbe504d4d4cdb9ae4a7305fbc"><td class="memItemLeft" align="right" valign="top">Traits::MatrixL&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1LLT.html#afb5490bbbe504d4d4cdb9ae4a7305fbc">matrixL</a> () const</td></tr>
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<tr class="memitem:ad5a1ff21b04aa9335996673b0ad61517"><td class="memItemLeft" align="right" valign="top">const MatrixType &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1LLT.html#ad5a1ff21b04aa9335996673b0ad61517">matrixLLT</a> () const</td></tr>
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<tr class="memitem:ad5d56462f3a9823723814acb0834983d"><td class="memItemLeft" align="right" valign="top">Traits::MatrixU&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1LLT.html#ad5d56462f3a9823723814acb0834983d">matrixU</a> () const</td></tr>
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<tr class="memitem:a56b1b914d7bd101a474c325327e17049"><td class="memTemplParams" colspan="2">template&lt;typename VectorType &gt; </td></tr>
<tr class="memitem:a56b1b914d7bd101a474c325327e17049"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1LLT.html">LLT</a>&lt; MatrixType_, UpLo_ &gt; &amp;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1LLT.html#a56b1b914d7bd101a474c325327e17049">rankUpdate</a> (const VectorType &amp;v, const RealScalar &amp;sigma)</td></tr>
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<tr class="memitem:a713323044a4b10e64e7fabe20d85b0c7"><td class="memItemLeft" align="right" valign="top">RealScalar&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1LLT.html#a713323044a4b10e64e7fabe20d85b0c7">rcond</a> () const</td></tr>
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<tr class="memitem:ae02929b4a8a1400ce605ca16d7774bc3"><td class="memItemLeft" align="right" valign="top">MatrixType&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1LLT.html#ae02929b4a8a1400ce605ca16d7774bc3">reconstructedMatrix</a> () const</td></tr>
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<tr class="memitem:ac3c983a7853b079f52ab53b9442a5256"><td class="memTemplParams" colspan="2">template&lt;typename Rhs &gt; </td></tr>
<tr class="memitem:ac3c983a7853b079f52ab53b9442a5256"><td class="memTemplItemLeft" align="right" valign="top">const <a class="el" href="classEigen_1_1Solve.html">Solve</a>&lt; <a class="el" href="classEigen_1_1LLT.html">LLT</a>, Rhs &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1LLT.html#ac3c983a7853b079f52ab53b9442a5256">solve</a> (const <a class="el" href="classEigen_1_1MatrixBase.html">MatrixBase</a>&lt; Rhs &gt; &amp;b) const</td></tr>
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<tr class="inherit_header pub_methods_classEigen_1_1SolverBase"><td colspan="2" onclick="javascript:toggleInherit('pub_methods_classEigen_1_1SolverBase')"><img src="closed.png" alt="-"/>&#160;Public Member Functions inherited from <a class="el" href="classEigen_1_1SolverBase.html">Eigen::SolverBase&lt; LLT&lt; MatrixType_, UpLo_ &gt; &gt;</a></td></tr>
<tr class="memitem:ae1025416bdb5a768f7213c67feb4dc33 inherit pub_methods_classEigen_1_1SolverBase"><td class="memItemLeft" align="right" valign="top">const AdjointReturnType&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SolverBase.html#ae1025416bdb5a768f7213c67feb4dc33">adjoint</a> () const</td></tr>
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<tr class="memitem:a1fbabe7f12bcbfba3b9a448b1f5e46fa inherit pub_methods_classEigen_1_1SolverBase"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1LLT.html">LLT</a>&lt; MatrixType_, UpLo_ &gt; &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SolverBase.html#a1fbabe7f12bcbfba3b9a448b1f5e46fa">derived</a> ()</td></tr>
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<tr class="memitem:afd4f3f1c57b7594b96a7e30f2974ea2e inherit pub_methods_classEigen_1_1SolverBase"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="classEigen_1_1LLT.html">LLT</a>&lt; MatrixType_, UpLo_ &gt; &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SolverBase.html#afd4f3f1c57b7594b96a7e30f2974ea2e">derived</a> () const</td></tr>
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<tr class="memitem:a7fd647d110487799205df6f99547879d inherit pub_methods_classEigen_1_1SolverBase"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="classEigen_1_1Solve.html">Solve</a>&lt; <a class="el" href="classEigen_1_1LLT.html">LLT</a>&lt; MatrixType_, UpLo_ &gt;, Rhs &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SolverBase.html#a7fd647d110487799205df6f99547879d">solve</a> (const <a class="el" href="classEigen_1_1MatrixBase.html">MatrixBase</a>&lt; Rhs &gt; &amp;b) const</td></tr>
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<tr class="memitem:a4d5e5baddfba3790ab1a5f247dcc4dc1 inherit pub_methods_classEigen_1_1SolverBase"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SolverBase.html#a4d5e5baddfba3790ab1a5f247dcc4dc1">SolverBase</a> ()</td></tr>
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<tr class="memitem:a70cf5cd1b31dbb4f4d61c436c83df6d3 inherit pub_methods_classEigen_1_1SolverBase"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="classEigen_1_1Transpose.html">ConstTransposeReturnType</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SolverBase.html#a70cf5cd1b31dbb4f4d61c436c83df6d3">transpose</a> () const</td></tr>
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<tr class="inherit_header pub_methods_structEigen_1_1EigenBase"><td colspan="2" onclick="javascript:toggleInherit('pub_methods_structEigen_1_1EigenBase')"><img src="closed.png" alt="-"/>&#160;Public Member Functions inherited from <a class="el" href="structEigen_1_1EigenBase.html">Eigen::EigenBase&lt; Derived &gt;</a></td></tr>
<tr class="memitem:a2d768a9877f5f69f49432d447b552bfe inherit pub_methods_structEigen_1_1EigenBase"><td class="memItemLeft" align="right" valign="top">EIGEN_CONSTEXPR <a class="el" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="structEigen_1_1EigenBase.html#a2d768a9877f5f69f49432d447b552bfe">cols</a> () const EIGEN_NOEXCEPT</td></tr>
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<tr class="memitem:a1fbabe7f12bcbfba3b9a448b1f5e46fa inherit pub_methods_structEigen_1_1EigenBase"><td class="memItemLeft" align="right" valign="top">Derived &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="structEigen_1_1EigenBase.html#a1fbabe7f12bcbfba3b9a448b1f5e46fa">derived</a> ()</td></tr>
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<tr class="memitem:afd4f3f1c57b7594b96a7e30f2974ea2e inherit pub_methods_structEigen_1_1EigenBase"><td class="memItemLeft" align="right" valign="top">const Derived &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="structEigen_1_1EigenBase.html#afd4f3f1c57b7594b96a7e30f2974ea2e">derived</a> () const</td></tr>
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<tr class="memitem:ac22eb0695d00edd7d4a3b2d0a98b81c2 inherit pub_methods_structEigen_1_1EigenBase"><td class="memItemLeft" align="right" valign="top">EIGEN_CONSTEXPR <a class="el" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="structEigen_1_1EigenBase.html#ac22eb0695d00edd7d4a3b2d0a98b81c2">rows</a> () const EIGEN_NOEXCEPT</td></tr>
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<tr class="memitem:ae106171b6fefd3f7af108a8283de36c9 inherit pub_methods_structEigen_1_1EigenBase"><td class="memItemLeft" align="right" valign="top">EIGEN_CONSTEXPR <a class="el" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="structEigen_1_1EigenBase.html#ae106171b6fefd3f7af108a8283de36c9">size</a> () const EIGEN_NOEXCEPT</td></tr>
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="inherited"></a>
Additional Inherited Members</h2></td></tr>
<tr class="inherit_header pub_types_structEigen_1_1EigenBase"><td colspan="2" onclick="javascript:toggleInherit('pub_types_structEigen_1_1EigenBase')"><img src="closed.png" alt="-"/>&#160;Public Types inherited from <a class="el" href="structEigen_1_1EigenBase.html">Eigen::EigenBase&lt; Derived &gt;</a></td></tr>
<tr class="memitem:a554f30542cc2316add4b1ea0a492ff02 inherit pub_types_structEigen_1_1EigenBase"><td class="memItemLeft" align="right" valign="top">typedef <a class="el" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Eigen::Index</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a></td></tr>
<tr class="memdesc:a554f30542cc2316add4b1ea0a492ff02 inherit pub_types_structEigen_1_1EigenBase"><td class="mdescLeft">&#160;</td><td class="mdescRight">The interface type of indices.  <a href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">More...</a><br /></td></tr>
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<h2 class="groupheader">Constructor &amp; Destructor Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#ae013aeead8f1f48c536ec0c3f1342bbd">&#9670;&nbsp;</a></span>LLT() <span class="overload">[1/3]</span></h2>

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template&lt;typename MatrixType_ , int UpLo_&gt; </div>
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<p>Default Constructor. </p>
<p>The default constructor is useful in cases in which the user intends to perform decompositions via LLT::compute(const MatrixType&amp;). </p>

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<p>Default Constructor with memory preallocation. </p>
<p>Like the default constructor but with preallocation of the internal data according to the specified problem <em>size</em>. </p><dl class="section see"><dt>See also</dt><dd><a class="el" href="classEigen_1_1LLT.html#ae013aeead8f1f48c536ec0c3f1342bbd" title="Default Constructor.">LLT()</a> </dd></dl>

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template&lt;typename MatrixType_ , int UpLo_&gt; </div>
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<p>Constructs a <a class="el" href="classEigen_1_1LLT.html" title="Standard Cholesky decomposition (LL^T) of a matrix and associated features.">LLT</a> factorization from a given matrix. </p>
<p>This overloaded constructor is provided for <a class="el" href="group__InplaceDecomposition.html">inplace decomposition </a> when <code>MatrixType</code> is a <a class="el" href="classEigen_1_1Ref.html" title="A matrix or vector expression mapping an existing expression.">Eigen::Ref</a>.</p>
<dl class="section see"><dt>See also</dt><dd>LLT(const EigenBase&amp;) </dd></dl>

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<h2 class="groupheader">Member Function Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#aa6ba8440554d9837b2bdb44b4c80c378">&#9670;&nbsp;</a></span>adjoint()</h2>

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<dl class="section return"><dt>Returns</dt><dd>the adjoint of <code>*this</code>, that is, a const reference to the decomposition itself as the underlying matrix is self-adjoint.</dd></dl>
<p>This method is provided for compatibility with other matrix decompositions, thus enabling generic code such as: </p><div class="fragment"><div class="line">x = decomposition.adjoint().solve(b) </div>
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<h2 class="memtitle"><span class="permalink"><a href="#a9dde013e51ed2b5cf2134daa3887d1e3">&#9670;&nbsp;</a></span>compute()</h2>

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<p>Computes / recomputes the Cholesky decomposition A = LL^* = U^*U of <em>matrix</em> </p>
<dl class="section return"><dt>Returns</dt><dd>a reference to *this</dd></dl>
<p>Example: </p><div class="fragment"><div class="line"><span class="preprocessor">#include &lt;iostream&gt;</span></div>
<div class="line"><span class="preprocessor">#include &lt;Eigen/Dense&gt;</span></div>
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<div class="line"><span class="keywordtype">int</span> main()</div>
<div class="line">{</div>
<div class="line">   <a class="code" href="classEigen_1_1Matrix.html">Eigen::Matrix2f</a> A, b;</div>
<div class="line">   <a class="code" href="classEigen_1_1LLT.html">Eigen::LLT&lt;Eigen::Matrix2f&gt;</a> llt;</div>
<div class="line">   A &lt;&lt; 2, -1, -1, 3;</div>
<div class="line">   b &lt;&lt; 1, 2, 3, 1;</div>
<div class="line">   std::cout &lt;&lt; <span class="stringliteral">&quot;Here is the matrix A:\n&quot;</span> &lt;&lt; A &lt;&lt; std::endl;</div>
<div class="line">   std::cout &lt;&lt; <span class="stringliteral">&quot;Here is the right hand side b:\n&quot;</span> &lt;&lt; b &lt;&lt; std::endl;</div>
<div class="line">   std::cout &lt;&lt; <span class="stringliteral">&quot;Computing LLT decomposition...&quot;</span> &lt;&lt; std::endl;</div>
<div class="line">   llt.compute(A);</div>
<div class="line">   std::cout &lt;&lt; <span class="stringliteral">&quot;The solution is:\n&quot;</span> &lt;&lt; llt.<a class="code" href="classEigen_1_1LLT.html#ac3c983a7853b079f52ab53b9442a5256">solve</a>(b) &lt;&lt; std::endl;</div>
<div class="line">   A(1,1)++;</div>
<div class="line">   std::cout &lt;&lt; <span class="stringliteral">&quot;The matrix A is now:\n&quot;</span> &lt;&lt; A &lt;&lt; std::endl;</div>
<div class="line">   std::cout &lt;&lt; <span class="stringliteral">&quot;Computing LLT decomposition...&quot;</span> &lt;&lt; std::endl;</div>
<div class="line">   llt.compute(A);</div>
<div class="line">   std::cout &lt;&lt; <span class="stringliteral">&quot;The solution is now:\n&quot;</span> &lt;&lt; llt.<a class="code" href="classEigen_1_1LLT.html#ac3c983a7853b079f52ab53b9442a5256">solve</a>(b) &lt;&lt; std::endl;</div>
<div class="line">}</div>
<div class="ttc" id="aclassEigen_1_1LLT_html"><div class="ttname"><a href="classEigen_1_1LLT.html">Eigen::LLT</a></div><div class="ttdoc">Standard Cholesky decomposition (LL^T) of a matrix and associated features.</div><div class="ttdef"><b>Definition:</b> LLT.h:70</div></div>
<div class="ttc" id="aclassEigen_1_1LLT_html_ac3c983a7853b079f52ab53b9442a5256"><div class="ttname"><a href="classEigen_1_1LLT.html#ac3c983a7853b079f52ab53b9442a5256">Eigen::LLT::solve</a></div><div class="ttdeci">const Solve&lt; LLT, Rhs &gt; solve(const MatrixBase&lt; Rhs &gt; &amp;b) const</div></div>
<div class="ttc" id="aclassEigen_1_1Matrix_html"><div class="ttname"><a href="classEigen_1_1Matrix.html">Eigen::Matrix</a></div><div class="ttdoc">The matrix class, also used for vectors and row-vectors.</div><div class="ttdef"><b>Definition:</b> Matrix.h:182</div></div>
</div><!-- fragment --><p> Output: </p><pre class="fragment">Here is the matrix A:
 2 -1
-1  3
Here is the right hand side b:
1 2
3 1
Computing LLT decomposition...
The solution is:
1.2 1.4
1.4 0.8
The matrix A is now:
 2 -1
-1  4
Computing LLT decomposition...
The solution is now:
    1  1.29
    1 0.571
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<h2 class="memtitle"><span class="permalink"><a href="#a1d05e5f1a15692959eb9e09d8959a5d5">&#9670;&nbsp;</a></span>info()</h2>

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<p>Reports whether previous computation was successful. </p>
<dl class="section return"><dt>Returns</dt><dd><code>Success</code> if computation was successful, <code>NumericalIssue</code> if the matrix.appears not to be positive definite. </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#afb5490bbbe504d4d4cdb9ae4a7305fbc">&#9670;&nbsp;</a></span>matrixL()</h2>

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<dl class="section return"><dt>Returns</dt><dd>a view of the lower triangular matrix L </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#ad5a1ff21b04aa9335996673b0ad61517">&#9670;&nbsp;</a></span>matrixLLT()</h2>

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<dl class="section return"><dt>Returns</dt><dd>the <a class="el" href="classEigen_1_1LLT.html" title="Standard Cholesky decomposition (LL^T) of a matrix and associated features.">LLT</a> decomposition matrix</dd></dl>
<p>TODO: document the storage layout </p>

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<h2 class="memtitle"><span class="permalink"><a href="#ad5d56462f3a9823723814acb0834983d">&#9670;&nbsp;</a></span>matrixU()</h2>

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<dl class="section return"><dt>Returns</dt><dd>a view of the upper triangular matrix U </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a56b1b914d7bd101a474c325327e17049">&#9670;&nbsp;</a></span>rankUpdate()</h2>

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template&lt;typename MatrixType_ , int UpLo_&gt; </div>
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          <td class="memname"><a class="el" href="classEigen_1_1LLT.html">LLT</a>&lt;MatrixType_,UpLo_&gt;&amp; <a class="el" href="classEigen_1_1LLT.html">Eigen::LLT</a>&lt; MatrixType_, UpLo_ &gt;::rankUpdate </td>
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<p>Performs a rank one update (or dowdate) of the current decomposition. If A = LL^* before the rank one update, then after it we have LL^* = A + sigma * v v^* where <em>v</em> must be a vector of same dimension. </p>

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<h2 class="memtitle"><span class="permalink"><a href="#a713323044a4b10e64e7fabe20d85b0c7">&#9670;&nbsp;</a></span>rcond()</h2>

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<dl class="section return"><dt>Returns</dt><dd>an estimate of the reciprocal condition number of the matrix of which <code>*this</code> is the Cholesky decomposition. </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#ae02929b4a8a1400ce605ca16d7774bc3">&#9670;&nbsp;</a></span>reconstructedMatrix()</h2>

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<dl class="section return"><dt>Returns</dt><dd>the matrix represented by the decomposition, i.e., it returns the product: L L^*. This function is provided for debug purpose. </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#ac3c983a7853b079f52ab53b9442a5256">&#9670;&nbsp;</a></span>solve()</h2>

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          <td class="memname">const <a class="el" href="classEigen_1_1Solve.html">Solve</a>&lt;<a class="el" href="classEigen_1_1LLT.html">LLT</a>, Rhs&gt; <a class="el" href="classEigen_1_1LLT.html">Eigen::LLT</a>&lt; MatrixType_, UpLo_ &gt;::solve </td>
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<dl class="section return"><dt>Returns</dt><dd>the solution x of \( A x = b \) using the current decomposition of A.</dd></dl>
<p>Since this <a class="el" href="classEigen_1_1LLT.html" title="Standard Cholesky decomposition (LL^T) of a matrix and associated features.">LLT</a> class assumes anyway that the matrix A is invertible, the solution theoretically exists and is unique regardless of b.</p>
<p>Example: </p><div class="fragment"><div class="line"><span class="keyword">typedef</span> Matrix&lt;float,Dynamic,2&gt; DataMatrix;</div>
<div class="line"><span class="comment">// let&#39;s generate some samples on the 3D plane of equation z = 2x+3y (with some noise)</span></div>
<div class="line">DataMatrix samples = DataMatrix::Random(12,2);</div>
<div class="line"><a class="code" href="group__matrixtypedefs.html#ga8028d921d43acd5605eabad41c254ef2">VectorXf</a> elevations = 2*samples.col(0) + 3*samples.col(1) + <a class="code" href="classEigen_1_1DenseBase.html#ae814abb451b48ed872819192dc188c19">VectorXf::Random</a>(12)*0.1;</div>
<div class="line"><span class="comment">// and let&#39;s solve samples * [x y]^T = elevations in least square sense:</span></div>
<div class="line">Matrix&lt;float,2,1&gt; xy</div>
<div class="line"> = (samples.adjoint() * samples).llt().solve((samples.adjoint()*elevations));</div>
<div class="line">cout &lt;&lt; xy &lt;&lt; endl;</div>
<div class="ttc" id="aclassEigen_1_1DenseBase_html_ae814abb451b48ed872819192dc188c19"><div class="ttname"><a href="classEigen_1_1DenseBase.html#ae814abb451b48ed872819192dc188c19">Eigen::DenseBase::Random</a></div><div class="ttdeci">static const RandomReturnType Random()</div><div class="ttdef"><b>Definition:</b> Random.h:114</div></div>
<div class="ttc" id="agroup__matrixtypedefs_html_ga8028d921d43acd5605eabad41c254ef2"><div class="ttname"><a href="group__matrixtypedefs.html#ga8028d921d43acd5605eabad41c254ef2">Eigen::VectorXf</a></div><div class="ttdeci">Matrix&lt; float, Dynamic, 1 &gt; VectorXf</div><div class="ttdoc">Dynamic×1 vector of type float.</div><div class="ttdef"><b>Definition:</b> Matrix.h:500</div></div>
</div><!-- fragment --><p> Output: </p><pre class="fragment">2.02
2.97
</pre><dl class="section see"><dt>See also</dt><dd>solveInPlace(), <a class="el" href="classEigen_1_1MatrixBase.html#a90c45f7a30265df792d5aeaddead2635">MatrixBase::llt()</a>, <a class="el" href="classEigen_1_1SelfAdjointView.html#a405e810491642a7f7b785f2ad6f93619">SelfAdjointView::llt()</a> </dd></dl>

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<hr/>The documentation for this class was generated from the following file:<ul>
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